MUSCL reconstruction and Haar wavelets (Q887360)

This paper deals with the numerical solution of hyperbolic problems of scalar conservation laws in one space dimension from computational fluid dynamics. Using as a base the standard Godunov's scheme and introducing scaling function and multi-resolution formalism in the least-square sense, a novel representation of the so called high-order MUSCL difference schemes (monotone upstream-centered schemes for conservation laws) is presented. This results in reconstruction of the MUSCL as a set of wavelet corrections in a Haar wallet framework. For the case of inhomogeneous equations a new MUSCL-WB (well balanced) scheme for advection-reaction problem is derived and studied.